Indirect LUT Architecture

The core mechanism of indirect LUT architecture involves training a postdistorter in the feedback path rather than directly identifying the predistorter. The postdistorter is placed after the PA model or actual PA output, and its coefficients are adapted to minimize the error between the postdistorter output and the original predistorted signal. Once converged, these coefficients are copied directly to the predistorter LUT in the forward path.

• Assumes the PA nonlinearity is invertible
• Avoids the need for a PA inverse model during training
• Coefficient copy eliminates separate forward model identification

The feedback observation receiver must capture the PA output with sufficient fidelity to enable accurate postdistorter training. Key specifications include:

• Bandwidth: Must exceed the transmit signal bandwidth by 3-5x to capture odd-order intermodulation products
• Dynamic range: Typically 60-70 dB to resolve spectral regrowth below the noise floor
• Time alignment: Sub-sample delay compensation between reference and feedback paths is critical
• IQ imbalance: Feedback path impairments must be calibrated independently to avoid corrupting LUT coefficient estimates

The defining architectural feature of indirect LUT architecture is the coefficient copy from the postdistorter training block to the forward predistorter LUT. This operation occurs after each adaptation iteration or batch update.

• Copy rate: Typically synchronized with the LUT adaptation rate
• Atomicity: Hardware implementations often use ping-pong buffering to ensure seamless switching without transient distortion
• Validation: Some architectures include a convergence monitor that gates the copy operation, preventing updates when the postdistorter error exceeds a threshold

The copy mechanism assumes the PA characteristics are stationary between updates, making this architecture suitable for tracking slow thermal drift.

The error signal driving LUT adaptation is computed in the training domain rather than the predistortion domain. The postdistorter output is compared against the original predistorted signal (or the input signal delayed appropriately).

• Cost function: Typically least mean squares (LMS) or normalized LMS
• Error vector: Complex-valued difference capturing both AM-AM and AM-PM correction residuals
• Averaging: Block-based averaging over multiple samples reduces noise sensitivity
• Weighting: Signal-dependent weighting can prioritize high-power regions where nonlinearity is most severe

The indirect architecture exhibits inherent stability because the postdistorter training is a standard system identification problem operating on the PA output. Unlike direct learning architectures that adapt the predistorter in a closed loop with the PA, the ILA decouples adaptation from the forward signal path.

• Convergence guarantee: LMS-based adaptation converges to the Wiener solution under stationary conditions
• Step size sensitivity: Adaptation rate must balance tracking speed against steady-state coefficient jitter
• PA nonlinearity limits: Severe saturation with phase discontinuities can violate the invertibility assumption, causing convergence failure
• Oscillation prevention: Some implementations include momentum terms or leaky LMS to prevent coefficient drift

FPGA and ASIC implementations of indirect LUT architecture require careful partitioning of the forward and feedback datapaths.

• Forward path: High-speed LUT lookup with complex multiplication for predistortion application
• Feedback path: Lower-rate observation receiver with decimation filters
• Training processor: Dedicated DSP blocks or embedded processor for LMS updates
• Memory architecture: Dual-port RAM for simultaneous read (predistortion) and write (update) operations
• Latency budget: Total loop delay from PA output sampling to coefficient update must be characterized and compensated

Typical implementations achieve ACLR improvements of 15-25 dB for 20 MHz LTE signals with LUT sizes of 256-1024 entries.

The open-loop counterpart to indirect architecture where the LUT directly maps input envelope to complex gain without feedback comparison.

• Key difference: No post-distorter training path
• Advantage: Lower computational complexity
• Limitation: Cannot adapt to PA drift without external model updates
• Use case: Static or slowly-varying amplifier characteristics

The Least Mean Squares algorithm that drives coefficient adaptation in the indirect architecture's training path.

• Minimizes mean squared error between desired and actual PA output
• Iteratively updates LUT entries using gradient descent
• Convergence rate controlled by step size parameter
• Susceptible to adaptation noise at small step sizes
• Forms the mathematical backbone of the post-distorter training block

The computational procedure for deriving optimal predistortion values from measured PA input-output data to populate the indirect architecture's tables.

• Offline extraction: Uses captured time-domain waveforms
• Online extraction: Runs continuously during transmission
• Requires precise time alignment between input and feedback paths
• Outputs complex gain values that represent the inverse PA nonlinearity
• Critical for initial LUT population before adaptive refinement begins

The stable state where the indirect architecture's error signal has been minimized to an acceptable residual level.

• Indicates the LUT accurately models the inverse amplifier nonlinearity
• Convergence time depends on adaptation rate and initial conditions
• Monitored via normalized mean squared error (NMSE) metrics
• Premature convergence can trap coefficients in local minima
• Essential for guaranteeing consistent ACLR and EVM performance

A dual-buffer memory architecture that enables seamless coefficient updates in indirect learning systems without interrupting predistortion.

• Active table: Currently applying predistortion to the transmit path
• Shadow table: Being updated by the training algorithm in background
• Atomic swap: Buffers exchange roles upon update completion
• Eliminates transient glitches during coefficient transitions
• Essential for real-time adaptive systems requiring continuous transmission

The speed at which the indirect architecture updates coefficients, controlling the trade-off between tracking agility and steady-state noise.

• Fast adaptation: Quickly tracks thermal and aging effects but introduces jitter
• Slow adaptation: Smooth steady-state performance but poor transient response
• Typically implemented via step size in LMS-based updates
• Must be tuned for specific PA thermal time constants
• Critical parameter for maintaining stability in closed-loop operation